Block #390,325

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 2/5/2014, 2:25:21 AM · Difficulty 10.4222 · 6,434,580 confirmations

1CC
Cunningham Chain of the First Kind

A sequence where each prime is double the previous prime plus one.

Block Header
Block Hash
ff82de26abbf9d1aba1f2f1fc2f8573cec7edfeeccbd2f46db541c2a38c3f51c

Height

#390,325

Difficulty

10.422248

Transactions

2

Size

755 B

Version

2

Bits

0a6c1879

Nonce

69,287

Timestamp

2/5/2014, 2:25:21 AM

Confirmations

6,434,580

Merkle Root

53b7dd3b1adb54c2dafb7d099b1b2a48a4c5b5ec0d980a91779aadd3ff8ee623
Prime Chain Origin

This is the prime chain origin stored in the block header. It is a composite number (not prime itself) — it equals the first prime in the chain multiplied by a primorial. The origin anchors the entire chain to this specific block.

1.373 × 10⁹⁸(99-digit number)
13730887197551182898…30643617002763163519
Discovered Prime Numbers
p_k = 2^k × origin − 1

These are the actual prime numbers discovered by this block, computed using the verified Primecoin formula. Each number has been independently confirmed to pass the Fermat primality test. Use the FactorDB links to verify any number independently.

1
origin − 1
1.373 × 10⁹⁸(99-digit number)
13730887197551182898…30643617002763163519
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
2
2^1 × origin − 1
2.746 × 10⁹⁸(99-digit number)
27461774395102365797…61287234005526327039
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
3
2^2 × origin − 1
5.492 × 10⁹⁸(99-digit number)
54923548790204731595…22574468011052654079
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
4
2^3 × origin − 1
1.098 × 10⁹⁹(100-digit number)
10984709758040946319…45148936022105308159
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
5
2^4 × origin − 1
2.196 × 10⁹⁹(100-digit number)
21969419516081892638…90297872044210616319
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
6
2^5 × origin − 1
4.393 × 10⁹⁹(100-digit number)
43938839032163785276…80595744088421232639
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
7
2^6 × origin − 1
8.787 × 10⁹⁹(100-digit number)
87877678064327570552…61191488176842465279
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
8
2^7 × origin − 1
1.757 × 10¹⁰⁰(101-digit number)
17575535612865514110…22382976353684930559
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
9
2^8 × origin − 1
3.515 × 10¹⁰⁰(101-digit number)
35151071225731028221…44765952707369861119
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
10
2^9 × origin − 1
7.030 × 10¹⁰⁰(101-digit number)
70302142451462056442…89531905414739722239
Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 10 consecutive prime numbers forming a Cunningham Chain of the First Kind. The prime chain origin — the large number shown above — anchors the chain and is divisible by a primorial (the product of small primes), cryptographically tying these prime numbers to this specific block.

★★☆☆☆
Rarity
UncommonChain length 10

Roughly 1 in 100 blocks. Solid but expected in a healthy network.

How Primecoin's Proof-of-Work Constructs These Primes

Primecoin stores a value called the prime chain origin in each block. The miner found a large integer such that when divided by a primorial (the product of small primes: 2 × 3 × 5 × 7 × …), the result is the first prime in the chain. The origin is deliberately divisible by this primorial — that divisibility is part of the proof.

Prime Chain Origin = First Prime × Primorial (2·3·5·7·11·…)
Source: Primecoin prime.cpp — CheckPrimeProofOfWork()

This is why the origin has many small prime factors — those factors are the primorial divisor. The chain then extends from the first prime using the 1CC formula:

1CC: p₁ (first prime), p₂ = 2p₁ + 1, p₃ = 2p₂ + 1, …
Circulating Supply:57,843,323 XPM·at block #6,824,904 · updates every 60s
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